King Elrond?

[Phrim]

Interesting quote that randomly came across today... (ROTK Appendix A, pg 314):

The sons of Earendil were Elros and Elrond, the Peredhil or Half-elven. In them alone the line of the heroic chieftains of the Edain in the First Age was preserved; and after the fall of Gil-galad the lineage of the High-elven Kings was also in Middle-earth only represented by their descendants.

Is Tolkien implying that there *is* in fact a King of the High-elves after Gil-galad?